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function [seq] = arithdeco(code, count, len)
// This function decodes the given code using arithmetic coding
// Calling sequence
// SEQ = ARITHDECO(CODE, COUNT, LEN)
//
// Description
// SEQ = ARITHDECO(CODE, COUNT, LEN) decodes the given received seq (CODE) to message using arithmetic coding.
// COUNT is vector whihc gives information about the source statistics (i.e. frequency of each symbol in the source alphabet)
// CODE is the binary arithmetic code
// Source Alphabet is assumed to be {1,2,....N} where N is a positive integer
// Therefore, sequence should be finite and positive
// Length of the COUNT should match the length of the source alphabet
// Examples
// counts = [40 1 9];
// len = 11;
// seq = [1 3 2 1 1 1 3 3 1 1 2 ]
// code = arithenco(seq,counts);
// disp(code)
// dseq=arithdeco(code,counts,len)
// disp(dseq)
// disp(seq)
// Bibliography
// Sayood, K., Introduction to Data Compression, Morgan Kaufmann, 2000, Chapter 4, Section 4.4.3.
// See also
// arithenco
// Authors
// Pola Lakshmi Priyanka, IIT Bombay//
//*************************************************************************************************************************************//
//Input argument check
[outa,inpa]=argn(0);
if(~inpa==3)
error("comm:arithenco:Wrong number of Input Arguments");
end
[row_code,col_code]=size(code);
[row_sta,col_sta]=size(count);
// Check to make sure that sequence is 1D
if(~(row_code==1|col_code==1))
error("comm:arithenco: Invalid dimensions: Input Arithmetic Encoded Sequence should be 1D ");
end
// Check for source statistics matrix
if(~(row_sta==1|col_sta==1))
error("comm:arithenco: Invalid dimensions: Argument 2 should be 1D ");
end
if(~isreal(code) | or(code<0) )
error("comm:arithenco: Input sequence should be finite positive integer");
end
if(~isreal(count) | or(count<0) )
error("comm:arithenco: Source statistics should be finite positive integer");
end
if(~isreal(len) | or(len<=0) | ~isscalar(len))
error("comm:arithenco: length should be finite positive integer and scalar");
end
//Check the incoming orientation and adjust if necessary
if (row_code > 1),
code = code.';
end
if (row_sta > 1),
count = count.';
end
// Check if the given code is binary
for i=1:length(code)
if (~(code(i)==1 | code(i)==0 ))
error("comm:arithenco:Input Arithmetic Encoded Sequence is not binary");
end
end
[row_s,col_s]=size(code);
[row_c,col_c]=size(count);
//Calculate the cumulative count
cum_count=[0,cumsum(count)];
total_count=cum_count(length(cum_count));
//Initialization
m=ceil(log2(total_count)) + 2;
low=zeros(1,m);
up=ones(1,m);
dec_low=0;
dec_up=2^m-1;
seq= zeros(1,len);
seq_index=1;
k=m;
tag=code(1:m);
dec_tag=0;
value=0;
for i=1:length(tag)
dec_tag=dec_tag+tag(i)*2^(length(tag)-i);
end
//loop till you decode entire seq
while (seq_index <= len)
// Compute value
value =floor( ((dec_tag-dec_low+1)*total_count-1)/(dec_up-dec_low+1) );
//Decode the symbol and update it
c=find(cum_count <= value)
ptr=c(length(c))
seq(seq_index)=ptr;
seq_index=seq_index+1;
//Compute lower and upper bounds
dec_low_new = dec_low + floor( (dec_up-dec_low+1)*cum_count(ptr)/total_count );
dec_up = dec_low + floor( (dec_up-dec_low+1)*cum_count(ptr+1)/total_count )-1;
dec_low = dec_low_new;
for i=1:m
low(i)=strtod(part(dec2bin(dec_low,m),i))
end
for i=1:m
up(i)=strtod(part(dec2bin(dec_up,m),i))
end
//Loop while E1, E2 or E3 condition
while(isequal(low(1),up(1))) | (isequal(low(2),1) & isequal(up(2),0))
if (k==length(code)) then
break;
end
k=k+1;
if isequal(low(1),up(1)) then //E1 or E2 holds
//Left shift
low=[low(2:m) 0];
up=[up(2:m) 1];
tag=[tag(2:m) code(k)];
elseif (isequal(low(2),1) & isequal(up(2),0)) then //for E3
//left shift
low=[low(2:m),0];
up=[up(2:m),1];
tag=[tag(2:m) code(k)];
low(1)=bitxor(low(1),1);
up(1)=bitxor(up(1),1);
tag(1)=bitxor(tag(1),1);
end
end
dec_low=0;dec_up=0;dec_tag=0;
for i=1:length(low)
dec_low=dec_low+low(i)*2^(length(low)-i);
dec_up=dec_up+up(i)*2^(length(up)-i);
dec_tag=dec_tag+tag(i)*2^(length(tag)-i);
end
end
endfunction
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